IODS course project
Riku Turkki
About the project
In this project I’ll learn the basics of MarkDown and git/GitHub. Here’s a link to my IODS-project GitHub page
Regression and model validation
Haven’t done this excercise :(
Logistic regression
Haven’t done this excercise ):
Clustering and classification
The topics of this chapter - clustering and classification - are handy and visual tools of exploring statistical data. Clustering means that some points (or observations) of the data are in some sense closer to each other than some other points. In other words, the data points do not comprise a homogeneous sample, but instead, it is somehow clustered.
In general, the clustering methods try to find these clusters (or groups) from the data. One of the most typical clustering methods is called k-means clustering. Also hierarchical clustering methods quite popular, giving tree-like dendrograms as their main output.
As such, clusters are easy to find, but what might be the “right” number of clusters? It is not always clear. And how to give these clusters names and interpretations?
Based on a successful clustering, we may try to classify new observations to these clusters and hence validate the results of clustering. Another way is to use various forms of discriminant analysis, which operates with the (now) known clusters, asking: “what makes the difference(s) between these groups (clusters)?”
In the connection of these methods, we also discuss the topic of distance (or dissimilarity or similarity) measures. There are lots of other measures than just the ordinary Euclidean distance, although it is one of the most important ones. Several discrete and even binary measures exist and are widely used for different purposes in various disciplines.
Point 2
## crim zn indus chas nox rm age dis rad tax ptratio black
## 1 0.00632 18 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 396.90
## 2 0.02731 0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 396.90
## 3 0.02729 0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 392.83
## 4 0.03237 0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 394.63
## 5 0.06905 0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 396.90
## 6 0.02985 0 2.18 0 0.458 6.430 58.7 6.0622 3 222 18.7 394.12
## lstat medv
## 1 4.98 24.0
## 2 9.14 21.6
## 3 4.03 34.7
## 4 2.94 33.4
## 5 5.33 36.2
## 6 5.21 28.7## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...## [1] 506 14Point 3
## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08204 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio black
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## lstat medv
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00Comments on point 3
Based on the scatter plot it seems that variables rm and lstat have a moderate anticorrelation (r = -0.614) whereas rm and medv seems to have positive correlation (r = 0.695). In addition, variable indus seems to have rather strong correlation with tax and nox (r = 0.721 and r = 0.764 respectively). dis weighted mean of distances to five Boston employment centres.
nox = nitrogen oxides concentration (parts per 10 million).
rm = average number of rooms per dwelling.
tax = full-value property-tax rate per $10,000.
lstat = lower status of the population (percent).
medv = median value of owner-occupied homes in $1000s.
Point 4
## crim zn indus
## Min. :-0.419367 Min. :-0.48724 Min. :-1.5563
## 1st Qu.:-0.410563 1st Qu.:-0.48724 1st Qu.:-0.8668
## Median :-0.390280 Median :-0.48724 Median :-0.2109
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.007389 3rd Qu.: 0.04872 3rd Qu.: 1.0150
## Max. : 9.924110 Max. : 3.80047 Max. : 2.4202
## chas nox rm age
## Min. :-0.2723 Min. :-1.4644 Min. :-3.8764 Min. :-2.3331
## 1st Qu.:-0.2723 1st Qu.:-0.9121 1st Qu.:-0.5681 1st Qu.:-0.8366
## Median :-0.2723 Median :-0.1441 Median :-0.1084 Median : 0.3171
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.:-0.2723 3rd Qu.: 0.5981 3rd Qu.: 0.4823 3rd Qu.: 0.9059
## Max. : 3.6648 Max. : 2.7296 Max. : 3.5515 Max. : 1.1164
## dis rad tax ptratio
## Min. :-1.2658 Min. :-0.9819 Min. :-1.3127 Min. :-2.7047
## 1st Qu.:-0.8049 1st Qu.:-0.6373 1st Qu.:-0.7668 1st Qu.:-0.4876
## Median :-0.2790 Median :-0.5225 Median :-0.4642 Median : 0.2746
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6617 3rd Qu.: 1.6596 3rd Qu.: 1.5294 3rd Qu.: 0.8058
## Max. : 3.9566 Max. : 1.6596 Max. : 1.7964 Max. : 1.6372
## black lstat medv
## Min. :-3.9033 Min. :-1.5296 Min. :-1.9063
## 1st Qu.: 0.2049 1st Qu.:-0.7986 1st Qu.:-0.5989
## Median : 0.3808 Median :-0.1811 Median :-0.1449
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4332 3rd Qu.: 0.6024 3rd Qu.: 0.2683
## Max. : 0.4406 Max. : 3.5453 Max. : 2.9865Comments on point 4
As can be seen from the plot above scaling the data frame obviously preseves the shape and distribution, however, the mean values are now set to zero and standard deviation to 1.
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## intersect, setdiff, setequal, unionPoint 5
Point 6
## predicted
## correct low med_low med_high high
## low 18 4 1 0
## med_low 5 12 14 0
## med_high 1 5 22 2
## high 0 0 1 17## Loading required package: lattice## Confusion Matrix and Statistics
##
## predicted
## correct low med_low med_high high
## low 18 4 1 0
## med_low 5 12 14 0
## med_high 1 5 22 2
## high 0 0 1 17
##
## Overall Statistics
##
## Accuracy : 0.6765
## 95% CI : (0.5766, 0.7658)
## No Information Rate : 0.3725
## P-Value [Acc > NIR] : 4.815e-10
##
## Kappa : 0.5639
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: low Class: med_low Class: med_high Class: high
## Sensitivity 0.7500 0.5714 0.5789 0.8947
## Specificity 0.9359 0.7654 0.8750 0.9880
## Pos Pred Value 0.7826 0.3871 0.7333 0.9444
## Neg Pred Value 0.9241 0.8732 0.7778 0.9762
## Prevalence 0.2353 0.2059 0.3725 0.1863
## Detection Rate 0.1765 0.1176 0.2157 0.1667
## Detection Prevalence 0.2255 0.3039 0.2941 0.1765
## Balanced Accuracy 0.8429 0.6684 0.7270 0.9413Comments on point 6
On overall, the classification with LDA seems to be working quite nicely. Classification accuracy is 0.765 (95% CI 0.6704, 0.8431) and Kappa value of 0.68 indicates substantial agreement.
Point 7
Comments on point 7
Based on the plot above k=2 is the optimal number of clusters.
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## Warning in cor(x, y, method = method, use = use): the standard deviation is
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Comments on point 7 contd.
Most obvious discriminating variables, bases on the plot above, are at least zn, nox, and tax. Blue group indicates cases where crime rates are higher and in red group the crime rates seems to be usually lower.
Bonus
Comments on Bonus
Strongest predictor variables are nox, tax, zn, and medv
Super-Bonus
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## layout## [1] 404 13## [1] 13 3Comments on super-bonus
Clustering (k=4) is not a perfect match with the real crime categories but is resembels it remarcably well.
Dimensionality reduction techniques — Data wrangling
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## between, first, lastDimensionality reduction techniques — Analysis
point 1
## 'data.frame': 155 obs. of 8 variables:
## $ Edu2.FM : num 1.007 0.997 0.983 0.989 0.969 ...
## $ Labo.FM : num 0.891 0.819 0.825 0.884 0.829 ...
## $ Edu.Exp : num 17.5 20.2 15.8 18.7 17.9 16.5 18.6 16.5 15.9 19.2 ...
## $ Life.Exp : num 81.6 82.4 83 80.2 81.6 80.9 80.9 79.1 82 81.8 ...
## $ GNI : int 64992 42261 56431 44025 45435 43919 39568 52947 42155 32689 ...
## $ Mat.Mor : int 4 6 6 5 6 7 9 28 11 8 ...
## $ Ado.Birth: num 7.8 12.1 1.9 5.1 6.2 3.8 8.2 31 14.5 25.3 ...
## $ Parli.F : num 39.6 30.5 28.5 38 36.9 36.9 19.9 19.4 28.2 31.4 ...The dataset human contains information regarding health, education, and govermental status collected from 155 countries. Short variable descriptions:
Edu2.FM: People with secondary education (female / male)
Labo.FM: Labour force participation rate (female / male)
Edu.Exp: Expected years of education
Life.Exp: Life expectancy at birth
GNI: Gross national income per capita
Mat.Mor: Maternal mortality ratio
Ado.Birth: Adolecent birth rate
Parli.F: Percent representation in parliament
For more detailed information please see: http://hdr.undp.org/sites/default/files/hdr2015_technical_notes.pdf
point 2
Brief comments on the data based on the plot above.
- Life expectancy has a strong correlations with education and strong negative correlation with maternal mortality and adolecent birth rate.
- Similarly GNI seem to correlate well with education and life expectancy. *Adolecent birth rate and maternal mortality are stronly linked.
- Interestingly percent precentation parliment doesn’t seem to correlate strongly with any of the variables.
point 3
## Warning in arrows(0, 0, y[, 1L] * 0.8, y[, 2L] * 0.8, col = col[2L], length
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Without scaling the above PCA biplot is dominated solely by GNI due to it’s large absolut values and variance.
point 4
After normalizing the variables the underlying effect of individual variables can be seen from the biplot above more clearly.
point 5
The first PC seems to capture nicely a transition between countries that have high life expectancy, high expected time of education, high women education, high GNI and low maternal mortality and low adolecent birth rate to those with opposite values. The second PC seems to aling with percent representation in parliament and labour force participation rate (female / male). As a note Nordic countries cluster to top-left corner indicating high value in both PC1 and PC2.
point 6
## 'data.frame': 300 obs. of 36 variables:
## $ breakfast : Factor w/ 2 levels "breakfast","Not.breakfast": 1 1 2 2 1 2 1 2 1 1 ...
## $ tea.time : Factor w/ 2 levels "Not.tea time",..: 1 1 2 1 1 1 2 2 2 1 ...
## $ evening : Factor w/ 2 levels "evening","Not.evening": 2 2 1 2 1 2 2 1 2 1 ...
## $ lunch : Factor w/ 2 levels "lunch","Not.lunch": 2 2 2 2 2 2 2 2 2 2 ...
## $ dinner : Factor w/ 2 levels "dinner","Not.dinner": 2 2 1 1 2 1 2 2 2 2 ...
## $ always : Factor w/ 2 levels "always","Not.always": 2 2 2 2 1 2 2 2 2 2 ...
## $ home : Factor w/ 2 levels "home","Not.home": 1 1 1 1 1 1 1 1 1 1 ...
## $ work : Factor w/ 2 levels "Not.work","work": 1 1 2 1 1 1 1 1 1 1 ...
## $ tearoom : Factor w/ 2 levels "Not.tearoom",..: 1 1 1 1 1 1 1 1 1 2 ...
## $ friends : Factor w/ 2 levels "friends","Not.friends": 2 2 1 2 2 2 1 2 2 2 ...
## $ resto : Factor w/ 2 levels "Not.resto","resto": 1 1 2 1 1 1 1 1 1 1 ...
## $ pub : Factor w/ 2 levels "Not.pub","pub": 1 1 1 1 1 1 1 1 1 1 ...
## $ Tea : Factor w/ 3 levels "black","Earl Grey",..: 1 1 2 2 2 2 2 1 2 1 ...
## $ How : Factor w/ 4 levels "alone","lemon",..: 1 3 1 1 1 1 1 3 3 1 ...
## $ sugar : Factor w/ 2 levels "No.sugar","sugar": 2 1 1 2 1 1 1 1 1 1 ...
## $ how : Factor w/ 3 levels "tea bag","tea bag+unpackaged",..: 1 1 1 1 1 1 1 1 2 2 ...
## $ where : Factor w/ 3 levels "chain store",..: 1 1 1 1 1 1 1 1 2 2 ...
## $ price : Factor w/ 6 levels "p_branded","p_cheap",..: 4 6 6 6 6 3 6 6 5 5 ...
## $ age : int 39 45 47 23 48 21 37 36 40 37 ...
## $ sex : Factor w/ 2 levels "F","M": 2 1 1 2 2 2 2 1 2 2 ...
## $ SPC : Factor w/ 7 levels "employee","middle",..: 2 2 4 6 1 6 5 2 5 5 ...
## $ Sport : Factor w/ 2 levels "Not.sportsman",..: 2 2 2 1 2 2 2 2 2 1 ...
## $ age_Q : Factor w/ 5 levels "15-24","25-34",..: 3 4 4 1 4 1 3 3 3 3 ...
## $ frequency : Factor w/ 4 levels "1/day","1 to 2/week",..: 1 1 3 1 3 1 4 2 3 3 ...
## $ escape.exoticism: Factor w/ 2 levels "escape-exoticism",..: 2 1 2 1 1 2 2 2 2 2 ...
## $ spirituality : Factor w/ 2 levels "Not.spirituality",..: 1 1 1 2 2 1 1 1 1 1 ...
## $ healthy : Factor w/ 2 levels "healthy","Not.healthy": 1 1 1 1 2 1 1 1 2 1 ...
## $ diuretic : Factor w/ 2 levels "diuretic","Not.diuretic": 2 1 1 2 1 2 2 2 2 1 ...
## $ friendliness : Factor w/ 2 levels "friendliness",..: 2 2 1 2 1 2 2 1 2 1 ...
## $ iron.absorption : Factor w/ 2 levels "iron absorption",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ feminine : Factor w/ 2 levels "feminine","Not.feminine": 2 2 2 2 2 2 2 1 2 2 ...
## $ sophisticated : Factor w/ 2 levels "Not.sophisticated",..: 1 1 1 2 1 1 1 2 2 1 ...
## $ slimming : Factor w/ 2 levels "No.slimming",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ exciting : Factor w/ 2 levels "exciting","No.exciting": 2 1 2 2 2 2 2 2 2 2 ...
## $ relaxing : Factor w/ 2 levels "No.relaxing",..: 1 1 2 2 2 2 2 2 2 2 ...
## $ effect.on.health: Factor w/ 2 levels "effect on health",..: 2 2 2 2 2 2 2 2 2 2 ...## [1] 300 36## breakfast tea.time evening lunch
## breakfast :144 Not.tea time:131 evening :103 lunch : 44
## Not.breakfast:156 tea time :169 Not.evening:197 Not.lunch:256
##
##
##
##
##
## dinner always home work
## dinner : 21 always :103 home :291 Not.work:213
## Not.dinner:279 Not.always:197 Not.home: 9 work : 87
##
##
##
##
##
## tearoom friends resto pub
## Not.tearoom:242 friends :196 Not.resto:221 Not.pub:237
## tearoom : 58 Not.friends:104 resto : 79 pub : 63
##
##
##
##
##
## Tea How sugar how
## black : 74 alone:195 No.sugar:155 tea bag :170
## Earl Grey:193 lemon: 33 sugar :145 tea bag+unpackaged: 94
## green : 33 milk : 63 unpackaged : 36
## other: 9
##
##
##
## where price age sex
## chain store :192 p_branded : 95 Min. :15.00 F:178
## chain store+tea shop: 78 p_cheap : 7 1st Qu.:23.00 M:122
## tea shop : 30 p_private label: 21 Median :32.00
## p_unknown : 12 Mean :37.05
## p_upscale : 53 3rd Qu.:48.00
## p_variable :112 Max. :90.00
##
## SPC Sport age_Q frequency
## employee :59 Not.sportsman:121 15-24:92 1/day : 95
## middle :40 sportsman :179 25-34:69 1 to 2/week: 44
## non-worker :64 35-44:40 +2/day :127
## other worker:20 45-59:61 3 to 6/week: 34
## senior :35 +60 :38
## student :70
## workman :12
## escape.exoticism spirituality healthy
## escape-exoticism :142 Not.spirituality:206 healthy :210
## Not.escape-exoticism:158 spirituality : 94 Not.healthy: 90
##
##
##
##
##
## diuretic friendliness iron.absorption
## diuretic :174 friendliness :242 iron absorption : 31
## Not.diuretic:126 Not.friendliness: 58 Not.iron absorption:269
##
##
##
##
##
## feminine sophisticated slimming
## feminine :129 Not.sophisticated: 85 No.slimming:255
## Not.feminine:171 sophisticated :215 slimming : 45
##
##
##
##
##
## exciting relaxing effect.on.health
## exciting :116 No.relaxing:113 effect on health : 66
## No.exciting:184 relaxing :187 No.effect on health:234
##
##
##
##
## ## Warning: attributes are not identical across measure variables; they will
## be dropped
##
## Call:
## MCA(X = tea, graph = FALSE)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6
## Variance 0.231 0.187 0.169 0.149 0.135 0.130
## % of var. 23.078 18.651 16.911 14.922 13.478 12.959
## Cumulative % of var. 23.078 41.729 58.641 73.563 87.041 100.000
##
## Individuals (the 10 first)
## Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3
## 1 | 0.011 0.000 0.000 | -0.841 1.265 0.925 | 0.186
## 2 | -0.738 0.787 0.886 | -0.012 0.000 0.000 | 0.131
## 3 | -0.121 0.021 0.018 | 0.562 0.565 0.386 | -0.328
## 4 | 0.314 0.143 0.134 | -0.366 0.240 0.182 | 0.291
## 5 | 0.252 0.091 0.049 | -0.157 0.044 0.019 | -0.621
## 6 | -0.118 0.020 0.020 | -0.051 0.005 0.004 | 0.269
## 7 | -0.422 0.257 0.239 | -0.526 0.495 0.372 | 0.164
## 8 | -0.121 0.021 0.018 | 0.562 0.565 0.386 | -0.328
## 9 | -0.062 0.006 0.004 | -0.256 0.117 0.062 | -0.057
## 10 | -0.108 0.017 0.012 | -0.427 0.326 0.187 | -0.400
## ctr cos2
## 1 0.068 0.045 |
## 2 0.034 0.028 |
## 3 0.212 0.131 |
## 4 0.167 0.115 |
## 5 0.760 0.298 |
## 6 0.142 0.101 |
## 7 0.053 0.036 |
## 8 0.212 0.131 |
## 9 0.006 0.003 |
## 10 0.315 0.164 |
##
## Categories (the 10 first)
## Dim.1 ctr cos2 v.test Dim.2 ctr cos2
## home | -0.078 0.422 0.195 -7.636 | -0.030 0.076 0.028
## Not.home | 2.511 13.660 0.195 7.636 | 0.956 2.448 0.028
## evening | 0.594 8.761 0.185 7.432 | 0.169 0.871 0.015
## Not.evening | -0.311 4.580 0.185 -7.432 | -0.088 0.456 0.015
## breakfast | -0.455 7.163 0.191 -7.552 | -0.640 17.574 0.378
## Not.breakfast | 0.420 6.612 0.191 7.552 | 0.591 16.222 0.378
## No.sugar | -0.603 13.557 0.388 -10.776 | 0.395 7.194 0.167
## sugar | 0.644 14.492 0.388 10.776 | -0.422 7.691 0.167
## F | -0.371 5.890 0.201 -7.744 | 0.542 15.564 0.428
## M | 0.541 8.594 0.201 7.744 | -0.791 22.709 0.428
## v.test Dim.3 ctr cos2 v.test
## home -2.906 | -0.124 1.468 0.497 -12.186 |
## Not.home 2.906 | 4.007 47.475 0.497 12.186 |
## evening 2.107 | -0.914 28.264 0.437 -11.427 |
## Not.evening -2.107 | 0.478 14.777 0.437 11.427 |
## breakfast -10.634 | -0.134 0.855 0.017 -2.234 |
## Not.breakfast 10.634 | 0.124 0.789 0.017 2.234 |
## No.sugar 7.057 | -0.026 0.036 0.001 -0.472 |
## sugar -7.057 | 0.028 0.038 0.001 0.472 |
## F 11.316 | -0.033 0.064 0.002 -0.690 |
## M -11.316 | 0.048 0.093 0.002 0.690 |
##
## Categorical variables (eta2)
## Dim.1 Dim.2 Dim.3
## home | 0.195 0.028 0.497 |
## evening | 0.185 0.015 0.437 |
## breakfast | 0.191 0.378 0.017 |
## sugar | 0.388 0.167 0.001 |
## sex | 0.201 0.428 0.002 |
## healthy | 0.225 0.103 0.062 |
Comments on MCA analysis: * Based on the plot above it seems that males are drinking their tea with sugar more often than females. * For some reason variable Not Home is clearly separate from other variables (maybe because there’s only really few of those that are not drinking tea at home). * Another interesting note from the plot is that those who are healthy tend to drink tea more often during breakfast whereas those who are not healthy drink more often during evenings.
Comments on point 2
The dataset contains 506 obersvations and 14 variables describing crime statistic in Boston area. Description of dataset variables ca be found from here